{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tutorial \n", "\n", "Let us consider chapter 7 of the excellent treatise on the subject of Exponential Smoothing By Hyndman and Athanasopoulos [1].\n", "We will work through all the examples in the chapter as they unfold.\n", "\n", "[1] [Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2014.](https://www.otexts.org/fpp/7)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Exponential smoothing\n", "\n", "First we load some data. We have included the R data in the notebook for expedience." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:15.020317Z", "start_time": "2017-12-07T12:39:14.263100Z" } }, "outputs": [], "source": [ "import os\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from statsmodels.tsa.api import ExponentialSmoothing, SimpleExpSmoothing, Holt\n", "\n", "data = [446.6565, 454.4733, 455.663 , 423.6322, 456.2713, 440.5881, 425.3325, 485.1494, 506.0482, 526.792 , 514.2689, 494.211 ]\n", "index= pd.date_range(start='1996', end='2008', freq='A')\n", "oildata = pd.Series(data, index)\n", "\n", "data = [17.5534, 21.86 , 23.8866, 26.9293, 26.8885, 28.8314, 30.0751, 30.9535, 30.1857, 31.5797, 32.5776, 33.4774, 39.0216, 41.3864, 41.5966]\n", "index= pd.date_range(start='1990', end='2005', freq='A')\n", "air = pd.Series(data, index)\n", "\n", "data = [263.9177, 268.3072, 260.6626, 266.6394, 277.5158, 283.834 , 290.309 , 292.4742, 300.8307, 309.2867, 318.3311, 329.3724, 338.884 , 339.2441, 328.6006, 314.2554, 314.4597, 321.4138, 329.7893, 346.3852, 352.2979, 348.3705, 417.5629, 417.1236, 417.7495, 412.2339, 411.9468, 394.6971, 401.4993, 408.2705, 414.2428]\n", "index= pd.date_range(start='1970', end='2001', freq='A')\n", "livestock2 = pd.Series(data, index)\n", "\n", "data = [407.9979 , 403.4608, 413.8249, 428.105 , 445.3387, 452.9942, 455.7402]\n", "index= pd.date_range(start='2001', end='2008', freq='A')\n", "livestock3 = pd.Series(data, index)\n", "\n", "data = [41.7275, 24.0418, 32.3281, 37.3287, 46.2132, 29.3463, 36.4829, 42.9777, 48.9015, 31.1802, 37.7179, 40.4202, 51.2069, 31.8872, 40.9783, 43.7725, 55.5586, 33.8509, 42.0764, 45.6423, 59.7668, 35.1919, 44.3197, 47.9137]\n", "index= pd.date_range(start='2005', end='2010-Q4', freq='QS-OCT')\n", "aust = pd.Series(data, index)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simple Exponential Smoothing\n", "Lets use Simple Exponential Smoothing to forecast the below oil data." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:15.189907Z", "start_time": "2017-12-07T12:39:15.022229Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Figure 7.1: Oil production in Saudi Arabia from 1996 to 2007.\n" ] } ], "source": [ "ax=oildata.plot()\n", "ax.set_xlabel(\"Year\")\n", "ax.set_ylabel(\"Oil (millions of tonnes)\")\n", "plt.show()\n", "print(\"Figure 7.1: Oil production in Saudi Arabia from 1996 to 2007.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we run three variants of simple exponential smoothing:\n", "1. In ```fit1``` we do not use the auto optimization but instead choose to explicitly provide the model with the $\\alpha=0.2$ parameter\n", "2. In ```fit2``` as above we choose an $\\alpha=0.6$\n", "3. In ```fit3``` we allow statsmodels to automatically find an optimized $\\alpha$ value for us. This is the recommended approach." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:15.785068Z", "start_time": "2017-12-07T12:39:15.191930Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fit1 = SimpleExpSmoothing(oildata).fit(smoothing_level=0.2,optimized=False)\n", "fcast1 = fit1.forecast(3).rename(r'$\\alpha=0.2$')\n", "fit2 = SimpleExpSmoothing(oildata).fit(smoothing_level=0.6,optimized=False)\n", "fcast2 = fit2.forecast(3).rename(r'$\\alpha=0.6$')\n", "fit3 = SimpleExpSmoothing(oildata).fit()\n", "fcast3 = fit3.forecast(3).rename(r'$\\alpha=%s$'%fit3.model.params['smoothing_level'])\n", "\n", "ax = oildata.plot(marker='o', color='black', figsize=(12,8))\n", "fcast1.plot(marker='o', ax=ax, color='blue', legend=True)\n", "fit1.fittedvalues.plot(marker='o', ax=ax, color='blue')\n", "fcast2.plot(marker='o', ax=ax, color='red', legend=True)\n", "\n", "fit2.fittedvalues.plot(marker='o', ax=ax, color='red')\n", "fcast3.plot(marker='o', ax=ax, color='green', legend=True)\n", "fit3.fittedvalues.plot(marker='o', ax=ax, color='green')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Holt's Method\n", "\n", "Lets take a look at another example.\n", "This time we use air pollution data and the Holt's Method.\n", "We will fit three examples again.\n", "1. In ```fit1``` we again choose not to use the optimizer and provide explicit values for $\\alpha=0.8$ and $\\beta=0.2$\n", "2. In ```fit2``` we do the same as in ```fit1``` but choose to use an exponential model rather than a Holt's additive model.\n", "3. In ```fit3``` we used a damped versions of the Holt's additive model but allow the dampening parameter $\\phi$ to be optimized while fixing the values for $\\alpha=0.8$ and $\\beta=0.2$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:16.114361Z", "start_time": "2017-12-07T12:39:15.786542Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fit1 = Holt(air).fit(smoothing_level=0.8, smoothing_slope=0.2, optimized=False)\n", "fcast1 = fit1.forecast(5).rename(\"Holt's linear trend\")\n", "fit2 = Holt(air, exponential=True).fit(smoothing_level=0.8, smoothing_slope=0.2, optimized=False)\n", "fcast2 = fit2.forecast(5).rename(\"Exponential trend\")\n", "fit3 = Holt(air, damped=True).fit(smoothing_level=0.8, smoothing_slope=0.2)\n", "fcast3 = fit3.forecast(5).rename(\"Additive damped trend\")\n", "\n", "ax = air.plot(color=\"black\", marker=\"o\", figsize=(12,8))\n", "fit1.fittedvalues.plot(ax=ax, color='blue')\n", "fcast1.plot(ax=ax, color='blue', marker=\"o\", legend=True)\n", "fit2.fittedvalues.plot(ax=ax, color='red')\n", "fcast2.plot(ax=ax, color='red', marker=\"o\", legend=True)\n", "fit3.fittedvalues.plot(ax=ax, color='green')\n", "fcast3.plot(ax=ax, color='green', marker=\"o\", legend=True)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Seasonally adjusted data\n", "Lets look at some seasonally adjusted livestock data. We fit five Holt's models.\n", "The below table allows us to compare results when we use exponential versus additive and damped versus non-damped.\n", " \n", "Note: ```fit4``` does not allow the parameter $\\phi$ to be optimized by providing a fixed value of $\\phi=0.98$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:16.605618Z", "start_time": "2017-12-07T12:39:16.116424Z" } }, "outputs": [ { "data": { "text/html": [ "
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SESHolt'sExponentialAdditiveMultiplicative
$\\alpha$1.0000000.9743060.9776340.9788260.974909
$\\beta$NaN0.0000000.0000000.0000000.000000
$\\phi$NaNNaNNaN0.9800000.981647
$l_0$263.918414258.882566260.341674257.355204258.951884
$b_0$NaN5.0107801.0137806.6442951.038144
SSE6761.3502186004.1382006104.1947476036.5550166081.995045
\n", "
" ], "text/plain": [ " SES Holt's Exponential Additive Multiplicative\n", "$\\alpha$ 1.000000 0.974306 0.977634 0.978826 0.974909\n", "$\\beta$ NaN 0.000000 0.000000 0.000000 0.000000\n", "$\\phi$ NaN NaN NaN 0.980000 0.981647\n", "$l_0$ 263.918414 258.882566 260.341674 257.355204 258.951884\n", "$b_0$ NaN 5.010780 1.013780 6.644295 1.038144\n", "SSE 6761.350218 6004.138200 6104.194747 6036.555016 6081.995045" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fit1 = SimpleExpSmoothing(livestock2).fit()\n", "fit2 = Holt(livestock2).fit()\n", "fit3 = Holt(livestock2,exponential=True).fit()\n", "fit4 = Holt(livestock2,damped=True).fit(damping_slope=0.98)\n", "fit5 = Holt(livestock2,exponential=True,damped=True).fit()\n", "params = ['smoothing_level', 'smoothing_slope', 'damping_slope', 'initial_level', 'initial_slope']\n", "results=pd.DataFrame(index=[r\"$\\alpha$\",r\"$\\beta$\",r\"$\\phi$\",r\"$l_0$\",\"$b_0$\",\"SSE\"] ,columns=['SES', \"Holt's\",\"Exponential\", \"Additive\", \"Multiplicative\"])\n", "results[\"SES\"] = [fit1.params[p] for p in params] + [fit1.sse]\n", "results[\"Holt's\"] = [fit2.params[p] for p in params] + [fit2.sse]\n", "results[\"Exponential\"] = [fit3.params[p] for p in params] + [fit3.sse]\n", "results[\"Additive\"] = [fit4.params[p] for p in params] + [fit4.sse]\n", "results[\"Multiplicative\"] = [fit5.params[p] for p in params] + [fit5.sse]\n", "results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plots of Seasonally Adjusted Data\n", "The following plots allow us to evaluate the level and slope/trend components of the above table's fits." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:17.105928Z", "start_time": "2017-12-07T12:39:16.607306Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Figure 7.4: Level and slope components for Holt’s linear trend method and the additive damped trend method.\n" ] } ], "source": [ "for fit in [fit2,fit4]:\n", " pd.DataFrame(np.c_[fit.level,fit.slope]).rename(\n", " columns={0:'level',1:'slope'}).plot(subplots=True)\n", "plt.show()\n", "print('Figure 7.4: Level and slope components for Holt’s linear trend method and the additive damped trend method.')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Comparison\n", "Here we plot a comparison Simple Exponential Smoothing and Holt's Methods for various additive, exponential and damped combinations. All of the models parameters will be optimized by statsmodels." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:18.038995Z", "start_time": "2017-12-07T12:39:17.108323Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Figure 7.5: Forecasting livestock, sheep in Asia: comparing forecasting performance of non-seasonal methods.\n" ] } ], "source": [ "fit1 = SimpleExpSmoothing(livestock2).fit()\n", "fcast1 = fit1.forecast(9).rename(\"SES\")\n", "fit2 = Holt(livestock2).fit()\n", "fcast2 = fit2.forecast(9).rename(\"Holt's\")\n", "fit3 = Holt(livestock2, exponential=True).fit()\n", "fcast3 = fit3.forecast(9).rename(\"Exponential\")\n", "fit4 = Holt(livestock2, damped=True).fit(damping_slope=0.98)\n", "fcast4 = fit4.forecast(9).rename(\"Additive Damped\")\n", "fit5 = Holt(livestock2, exponential=True, damped=True).fit()\n", "fcast5 = fit5.forecast(9).rename(\"Multiplicative Damped\")\n", "\n", "ax = livestock2.plot(color=\"black\", marker=\"o\", figsize=(12,8))\n", "livestock3.plot(ax=ax, color=\"black\", marker=\"o\", legend=False)\n", "fcast1.plot(ax=ax, color='red', legend=True)\n", "fcast2.plot(ax=ax, color='green', legend=True)\n", "fcast3.plot(ax=ax, color='blue', legend=True)\n", "fcast4.plot(ax=ax, color='cyan', legend=True)\n", "fcast5.plot(ax=ax, color='magenta', legend=True)\n", "ax.set_ylabel('Livestock, sheep in Asia (millions)')\n", "plt.show()\n", "print('Figure 7.5: Forecasting livestock, sheep in Asia: comparing forecasting performance of non-seasonal methods.')" ] }, { "cell_type": "markdown", "metadata": { "ExecuteTime": { "end_time": "2017-10-05T09:40:15.958575Z", "start_time": "2017-10-05T09:40:15.615Z" } }, "source": [ "## Holt's Winters Seasonal\n", "Finally we are able to run full Holt's Winters Seasonal Exponential Smoothing including a trend component and a seasonal component.\n", "statsmodels allows for all the combinations including as shown in the examples below:\n", "1. ```fit1``` additive trend, additive seasonal of period ```season_length=4``` and the use of a Box-Cox transformation.\n", "1. ```fit2``` additive trend, multiplicative seasonal of period ```season_length=4``` and the use of a Box-Cox transformation..\n", "1. ```fit3``` additive damped trend, additive seasonal of period ```season_length=4``` and the use of a Box-Cox transformation.\n", "1. ```fit4``` additive damped trend, multiplicative seasonal of period ```season_length=4``` and the use of a Box-Cox transformation.\n", "\n", "The plot shows the results and forecast for ```fit1``` and ```fit2```.\n", "The table allows us to compare the results and parameterizations." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:28.375871Z", "start_time": "2017-12-07T12:39:18.040674Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Figure 7.6: Forecasting international visitor nights in Australia using Holt-Winters method with both additive and multiplicative seasonality.\n" ] }, { "data": { "text/html": [ "
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AdditiveMultiplicativeAdditive DamMultiplica Dam
$\\alpha$4.546625e-013.659925e-016.788341e-090.000178
$\\beta$1.554872e-081.832850e-204.846709e-720.000178
$\\phi$NaNNaN9.431105e-010.913344
$\\gamma$5.243651e-012.657584e-141.084804e-060.000000
$l_0$1.421756e+011.454805e+011.415717e+0114.535054
$b_0$1.307577e-011.661245e-012.455367e-010.483855
SSE5.001711e+014.307070e+013.527454e+0139.683104
\n", "
" ], "text/plain": [ " Additive Multiplicative Additive Dam Multiplica Dam\n", "$\\alpha$ 4.546625e-01 3.659925e-01 6.788341e-09 0.000178\n", "$\\beta$ 1.554872e-08 1.832850e-20 4.846709e-72 0.000178\n", "$\\phi$ NaN NaN 9.431105e-01 0.913344\n", "$\\gamma$ 5.243651e-01 2.657584e-14 1.084804e-06 0.000000\n", "$l_0$ 1.421756e+01 1.454805e+01 1.415717e+01 14.535054\n", "$b_0$ 1.307577e-01 1.661245e-01 2.455367e-01 0.483855\n", "SSE 5.001711e+01 4.307070e+01 3.527454e+01 39.683104" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fit1 = ExponentialSmoothing(aust, seasonal_periods=4, trend='add', seasonal='add').fit(use_boxcox=True)\n", "fit2 = ExponentialSmoothing(aust, seasonal_periods=4, trend='add', seasonal='mul').fit(use_boxcox=True)\n", "fit3 = ExponentialSmoothing(aust, seasonal_periods=4, trend='add', seasonal='add', damped=True).fit(use_boxcox=True)\n", "fit4 = ExponentialSmoothing(aust, seasonal_periods=4, trend='add', seasonal='mul', damped=True).fit(use_boxcox=True)\n", "results=pd.DataFrame(index=[r\"$\\alpha$\",r\"$\\beta$\",r\"$\\phi$\",r\"$\\gamma$\",r\"$l_0$\",\"$b_0$\",\"SSE\"])\n", "params = ['smoothing_level', 'smoothing_slope', 'damping_slope', 'smoothing_seasonal', 'initial_level', 'initial_slope']\n", "results[\"Additive\"] = [fit1.params[p] for p in params] + [fit1.sse]\n", "results[\"Multiplicative\"] = [fit2.params[p] for p in params] + [fit2.sse]\n", "results[\"Additive Dam\"] = [fit3.params[p] for p in params] + [fit3.sse]\n", "results[\"Multiplica Dam\"] = [fit4.params[p] for p in params] + [fit4.sse]\n", "\n", "ax = aust.plot(figsize=(10,6), marker='o', color='black', title=\"Forecasts from Holt-Winters' multiplicative method\" )\n", "ax.set_ylabel(\"International visitor night in Australia (millions)\")\n", "ax.set_xlabel(\"Year\")\n", "fit1.fittedvalues.plot(ax=ax, style='--', color='red')\n", "fit2.fittedvalues.plot(ax=ax, style='--', color='green')\n", "\n", "fit1.forecast(8).rename('Holt-Winters (add-add-seasonal)').plot(ax=ax, style='--', marker='o', color='red', legend=True)\n", "fit2.forecast(8).rename('Holt-Winters (add-mul-seasonal)').plot(ax=ax, style='--', marker='o', color='green', legend=True)\n", "\n", "plt.show()\n", "print(\"Figure 7.6: Forecasting international visitor nights in Australia using Holt-Winters method with both additive and multiplicative seasonality.\")\n", "\n", "results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Internals\n", "It is possible to get at the internals of the Exponential Smoothing models. \n", "\n", "Here we show some tables that allow you to view side by side the original values $y_t$, the level $l_t$, the trend $b_t$, the season $s_t$ and the fitted values $\\hat{y}_t$." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:28.399765Z", "start_time": "2017-12-07T12:39:28.377215Z" } }, "outputs": [ { "data": { "text/html": [ "
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$\\hat{y}_t$$b_t$$l_t$$s_t$$y_t$
2005-01-0141.721337-34.96941449.317727-7.59337741.7275
2005-04-0124.190470-35.45263349.932262-25.83440924.0418
2005-07-0131.460236-36.53275651.126063-19.18295732.3281
2005-10-0136.634461-37.39766252.210086-15.20980237.3287
2006-01-0145.097507-38.46727753.476761-7.83729646.2132
2006-04-0127.191826-40.27626955.513789-27.01716829.3463
2006-07-0136.544154-40.62493556.224337-19.71375036.4829
2006-10-0141.449262-42.04173057.766008-15.52327642.9777
2007-01-0150.934293-41.54366057.536556-7.58868148.9015
2007-04-0131.418021-42.19771558.150830-26.87420531.1802
2007-07-0138.718199-42.30327258.362734-20.19176537.7179
2007-10-0144.140343-41.08546057.181495-14.98271440.4202
2008-01-0149.315503-42.96129758.852717-8.61965151.2069
2008-04-0132.306830-43.18629559.366679-27.30895331.8872
2008-07-0139.207327-44.82679561.095332-20.92528140.9783
2008-10-0144.551315-44.89908761.461719-17.31947143.7725
2009-01-0154.357802-46.19194962.816449-7.88137155.5586
2009-04-0135.153724-45.97977462.831666-28.44751333.8509
2009-07-0143.066191-46.22772763.082162-20.55034542.0764
2009-10-0145.871061-46.85204963.748292-17.99731645.6423
2010-01-0157.166318-48.77007865.777152-7.37175559.7668
2010-04-0136.761359-48.30780165.649392-29.81630335.1919
2010-07-0144.932303-48.79810566.118764-21.51692944.3197
2010-10-0148.399392-49.26922266.666696-18.52167047.9137
2011-01-0161.337554NaNNaNNaNNaN
2011-04-0137.242648NaNNaNNaNNaN
2011-07-0146.842316NaNNaNNaNNaN
2011-10-0151.004726NaNNaNNaNNaN
2012-01-0164.469960NaNNaNNaNNaN
2012-04-0139.776334NaNNaNNaNNaN
2012-07-0149.635147NaNNaNNaNNaN
2012-10-0153.900518NaNNaNNaNNaN
\n", "
" ], "text/plain": [ " $\\hat{y}_t$ $b_t$ $l_t$ $s_t$ $y_t$\n", "2005-01-01 41.721337 -34.969414 49.317727 -7.593377 41.7275\n", "2005-04-01 24.190470 -35.452633 49.932262 -25.834409 24.0418\n", "2005-07-01 31.460236 -36.532756 51.126063 -19.182957 32.3281\n", "2005-10-01 36.634461 -37.397662 52.210086 -15.209802 37.3287\n", "2006-01-01 45.097507 -38.467277 53.476761 -7.837296 46.2132\n", "2006-04-01 27.191826 -40.276269 55.513789 -27.017168 29.3463\n", "2006-07-01 36.544154 -40.624935 56.224337 -19.713750 36.4829\n", "2006-10-01 41.449262 -42.041730 57.766008 -15.523276 42.9777\n", "2007-01-01 50.934293 -41.543660 57.536556 -7.588681 48.9015\n", "2007-04-01 31.418021 -42.197715 58.150830 -26.874205 31.1802\n", "2007-07-01 38.718199 -42.303272 58.362734 -20.191765 37.7179\n", "2007-10-01 44.140343 -41.085460 57.181495 -14.982714 40.4202\n", "2008-01-01 49.315503 -42.961297 58.852717 -8.619651 51.2069\n", "2008-04-01 32.306830 -43.186295 59.366679 -27.308953 31.8872\n", "2008-07-01 39.207327 -44.826795 61.095332 -20.925281 40.9783\n", "2008-10-01 44.551315 -44.899087 61.461719 -17.319471 43.7725\n", "2009-01-01 54.357802 -46.191949 62.816449 -7.881371 55.5586\n", "2009-04-01 35.153724 -45.979774 62.831666 -28.447513 33.8509\n", "2009-07-01 43.066191 -46.227727 63.082162 -20.550345 42.0764\n", "2009-10-01 45.871061 -46.852049 63.748292 -17.997316 45.6423\n", "2010-01-01 57.166318 -48.770078 65.777152 -7.371755 59.7668\n", "2010-04-01 36.761359 -48.307801 65.649392 -29.816303 35.1919\n", "2010-07-01 44.932303 -48.798105 66.118764 -21.516929 44.3197\n", "2010-10-01 48.399392 -49.269222 66.666696 -18.521670 47.9137\n", "2011-01-01 61.337554 NaN NaN NaN NaN\n", "2011-04-01 37.242648 NaN NaN NaN NaN\n", "2011-07-01 46.842316 NaN NaN NaN NaN\n", "2011-10-01 51.004726 NaN NaN NaN NaN\n", "2012-01-01 64.469960 NaN NaN NaN NaN\n", "2012-04-01 39.776334 NaN NaN NaN NaN\n", "2012-07-01 49.635147 NaN NaN NaN NaN\n", "2012-10-01 53.900518 NaN NaN NaN NaN" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = pd.DataFrame(np.c_[aust, fit1.level, fit1.slope, fit1.season, fit1.fittedvalues],\n", " columns=[r'$y_t$',r'$l_t$',r'$b_t$',r'$s_t$',r'$\\hat{y}_t$'],index=aust.index)\n", "df.append(fit1.forecast(8).rename(r'$\\hat{y}_t$').to_frame(), sort=True)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:28.574783Z", "start_time": "2017-12-07T12:39:28.401234Z" } }, "outputs": [ { "data": { "text/html": [ "
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$\\hat{y}_t$$b_t$$l_t$$s_t$$y_t$
2005-01-0141.859612-36.52988851.2440660.81590941.7275
2005-04-0125.838333-35.86634850.7356770.49538424.0418
2005-07-0131.658927-37.28371552.0600970.61300032.3281
2005-10-0135.189404-39.16920554.1868960.66419637.3287
2006-01-0144.929187-40.30606755.7057760.81506846.2132
2006-04-0127.933714-42.08765957.7562370.49306429.3463
2006-07-0135.824584-43.10052359.1270930.61010636.4829
2006-10-0139.768835-45.64435161.9072030.66172042.9777
2007-01-0151.175036-45.12118761.8560660.81361048.9015
2007-04-0130.814546-46.40859563.1348750.49030931.1802
2007-07-0139.009285-46.38645863.3268570.60823937.7179
2007-10-0142.485965-46.17064263.1430230.66045740.4202
2008-01-0152.174108-46.75925063.7010070.81340351.2069
2008-04-0131.677199-47.83562564.8702150.48956531.8872
2008-07-0140.035687-49.23941666.4673980.60768940.9783
2008-10-0144.515949-49.57512467.0648690.65959643.7725
2009-01-0155.343449-50.60223568.1892000.81278555.5586
2009-04-0133.773122-51.51532669.2842310.48789033.8509
2009-07-0142.644252-52.02533669.9701970.60638842.0764
2009-10-0146.778369-52.31061270.3650880.65870845.6423
2010-01-0158.009128-54.09387672.2112420.81230759.7668
2010-04-0135.648414-54.49983272.9092170.48653035.1919
2010-07-0144.784337-55.16373573.6826810.60541444.3197
2010-10-0149.174394-55.38937774.0292050.65783947.9137
2011-01-0160.967448NaNNaNNaNNaN
2011-04-0136.993757NaNNaNNaNNaN
2011-07-0146.712314NaNNaNNaNNaN
2011-10-0151.482619NaNNaNNaNNaN
2012-01-0164.456291NaNNaNNaNNaN
2012-04-0139.017141NaNNaNNaNNaN
2012-07-0149.291639NaNNaNNaNNaN
2012-10-0154.319914NaNNaNNaNNaN
\n", "
" ], "text/plain": [ " $\\hat{y}_t$ $b_t$ $l_t$ $s_t$ $y_t$\n", "2005-01-01 41.859612 -36.529888 51.244066 0.815909 41.7275\n", "2005-04-01 25.838333 -35.866348 50.735677 0.495384 24.0418\n", "2005-07-01 31.658927 -37.283715 52.060097 0.613000 32.3281\n", "2005-10-01 35.189404 -39.169205 54.186896 0.664196 37.3287\n", "2006-01-01 44.929187 -40.306067 55.705776 0.815068 46.2132\n", "2006-04-01 27.933714 -42.087659 57.756237 0.493064 29.3463\n", "2006-07-01 35.824584 -43.100523 59.127093 0.610106 36.4829\n", "2006-10-01 39.768835 -45.644351 61.907203 0.661720 42.9777\n", "2007-01-01 51.175036 -45.121187 61.856066 0.813610 48.9015\n", "2007-04-01 30.814546 -46.408595 63.134875 0.490309 31.1802\n", "2007-07-01 39.009285 -46.386458 63.326857 0.608239 37.7179\n", "2007-10-01 42.485965 -46.170642 63.143023 0.660457 40.4202\n", "2008-01-01 52.174108 -46.759250 63.701007 0.813403 51.2069\n", "2008-04-01 31.677199 -47.835625 64.870215 0.489565 31.8872\n", "2008-07-01 40.035687 -49.239416 66.467398 0.607689 40.9783\n", "2008-10-01 44.515949 -49.575124 67.064869 0.659596 43.7725\n", "2009-01-01 55.343449 -50.602235 68.189200 0.812785 55.5586\n", "2009-04-01 33.773122 -51.515326 69.284231 0.487890 33.8509\n", "2009-07-01 42.644252 -52.025336 69.970197 0.606388 42.0764\n", "2009-10-01 46.778369 -52.310612 70.365088 0.658708 45.6423\n", "2010-01-01 58.009128 -54.093876 72.211242 0.812307 59.7668\n", "2010-04-01 35.648414 -54.499832 72.909217 0.486530 35.1919\n", "2010-07-01 44.784337 -55.163735 73.682681 0.605414 44.3197\n", "2010-10-01 49.174394 -55.389377 74.029205 0.657839 47.9137\n", "2011-01-01 60.967448 NaN NaN NaN NaN\n", "2011-04-01 36.993757 NaN NaN NaN NaN\n", "2011-07-01 46.712314 NaN NaN NaN NaN\n", "2011-10-01 51.482619 NaN NaN NaN NaN\n", "2012-01-01 64.456291 NaN NaN NaN NaN\n", "2012-04-01 39.017141 NaN NaN NaN NaN\n", "2012-07-01 49.291639 NaN NaN NaN NaN\n", "2012-10-01 54.319914 NaN NaN NaN NaN" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = pd.DataFrame(np.c_[aust, fit2.level, fit2.slope, fit2.season, fit2.fittedvalues], \n", " columns=[r'$y_t$',r'$l_t$',r'$b_t$',r'$s_t$',r'$\\hat{y}_t$'],index=aust.index)\n", "df.append(fit2.forecast(8).rename(r'$\\hat{y}_t$').to_frame(), sort=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally lets look at the levels, slopes/trends and seasonal components of the models." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:29.636548Z", "start_time": "2017-12-07T12:39:28.576279Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "states1 = pd.DataFrame(np.c_[fit1.level, fit1.slope, fit1.season], columns=['level','slope','seasonal'], index=aust.index)\n", "states2 = pd.DataFrame(np.c_[fit2.level, fit2.slope, fit2.season], columns=['level','slope','seasonal'], index=aust.index)\n", "fig, [[ax1, ax4],[ax2, ax5], [ax3, ax6]] = plt.subplots(3, 2, figsize=(12,8))\n", "states1[['level']].plot(ax=ax1)\n", "states1[['slope']].plot(ax=ax2)\n", "states1[['seasonal']].plot(ax=ax3)\n", "states2[['level']].plot(ax=ax4)\n", "states2[['slope']].plot(ax=ax5)\n", "states2[['seasonal']].plot(ax=ax6)\n", "plt.show()" ] } ], "metadata": { "anaconda-cloud": {}, "hide_input": false, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.6" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "toc": { "colors": { "hover_highlight": "#DAA520", "navigate_num": "#000000", "navigate_text": "#333333", "running_highlight": "#FF0000", "selected_highlight": "#FFD700", "sidebar_border": "#EEEEEE", "wrapper_background": "#FFFFFF" }, "moveMenuLeft": true, "nav_menu": { "height": "98px", "width": "252px" }, "navigate_menu": true, "number_sections": false, "sideBar": true, "threshold": 4, "toc_cell": false, "toc_section_display": "block", "toc_window_display": true, "widenNotebook": false } }, "nbformat": 4, "nbformat_minor": 1 }